On some conjectures of Askey (Q2774118)
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scientific article; zbMATH DE number 1713366
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some conjectures of Askey |
scientific article; zbMATH DE number 1713366 |
Statements
20 November 2002
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positive power series coefficients
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Darboux method of asymptotic analysis
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Gegenbauer polynomials
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0.8885031
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On some conjectures of Askey (English)
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Using the Darboux method of asymptotic analysis, it is shown that the coefficients of the power series expansions of the functions \(f(w)=(1-w)^{-c}(1-2xw+w^2)^{-c}\) and \((1+w)f(w), 1<c<2\), at \(w=0\) are positive if \(x\) lies in certain intervals. This partially answers some questions raised by Richard Askey.
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